III: Medium: Collaborative Research: Topological Data Analysis for Large Network Visualization

该项目利用拓扑方法来开发一类新的数据分析和可视化技术，以了解网络的结构。 网络通常用于对社会、生物和技术系统进行建模，并捕捉个人、企业和基因组实体之间的关系。了解如此庞大、复杂的数据源在包括脑连接组学、流行病学、执法、公共政策和营销在内的应用领域具有高度相关性和重要性。 这项研究将在多个数据源上进行评估，包括但不限于大型社交、通信和大脑网络数据集。此外，该项目中开发的新方法将被纳入不断增长的数据分析课程，通过开发研讨会进行分享，并作为主题继续吸引代表性不足的群体进入STEM领域和计算机科学。该项目解决的科学挑战是双重的：如何使用拓扑从数据中提取特征;以及如何设计有效的可视化来将这些特征传达给领域专家和决策者。 拓扑技术中心，这个项目提供了一个强大的理论基础，简化和总结复杂的数据，同时仍然保留关键的底层结构。它们还为面向任务的设计提供了基础，使我们能够控制可视化中显示的数据量，因此用户可以开发数据的忠实心理模型，促进信息发现。该项目侧重于两个研究议程。首先，它提出了一个丰富的身体的拓扑摘要技术提取和保存重要的拓扑特征内的大规模图形结构的网络，并获得紧凑和层次表示，适合于视觉探索。特征提取过程捕获系统中的复杂交互，描述所有尺度的特征，相对于噪声是鲁棒的，并且具有高效的计算。第二，本项目提出设计可视化，明确编码提取的拓扑结构，专注于调查技术，充分利用其属性的视觉隐喻开发。该项目的网站（http：//www.sci.utah.edu/networktdav）提供了更多的信息，并将提供已开发的工具和测试数据集。

This project leverages topological methods to develop a new class of data analysis and visualization techniques to understand the structure of networks. Networks are often used in modeling social, biological and technological systems, and capturing relationships among individuals, businesses, and genomic entities. Understanding such large, complex data sources is highly relevant and important in application areas including brain connectomics, epidemiology, law enforcement, public policy and marketing. The proposed research will be evaluated over multiple data sources, including but not limited to large social, communication and brain network datasets. Furthermore, the new approaches developed in this project will be integrated into growing data analysis curricula, shared through developing workshops, and used as topics to continue attracting underrepresented groups into STEM fields and computer science specifically. The scientific challenges this project addresses are two-fold: how to use topology to extract features from the data; and how to design effective visualizations to communicate these features to domain experts and decision makers. Topological techniques central to this project provide a strong theoretical basis for simplifying and summarizing complex data while still preserving critical underlying structures. They also provide a basis for task-oriented designs that allow us to control the volume of data to be displayed in visualizations, so users can develop faithful mental models of the data, facilitating information discovery. This project focuses on two research agendas. First, it proposes a rich body of topological summarization techniques to extract and preserve important topological features within large-scale graph-structured networks, and to obtain compact and hierarchical representations that are suitable for visual exploration. The feature extracting process captures complex interactions in the system, describes features at all scales, is robust with respect to noise, and has efficient computation. Second, this project proposes designing visualizations that encode the extracted topological structures explicitly, focusing on investigating techniques to fully exploit their properties in the visual metaphors to be developed. The project web site (http://www.sci.utah.edu/networktdav) provides additional information and will include access to developed tools and test data sets.